Problem: Find the zeros of the function. Enter the solutions from least to greatest. $g (x)=(-5x -1)(2x +8)$ $\text{lesser }x = $
For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(-5x -1)(2x +8)=0$. So either $(-5x -1)=0$ or $(2x +8)=0$ : $\begin{aligned} (1)&&-5x -1&=0 \\\\ &&-5x&=1 \\\\ &&x&=-\dfrac{1}{5} \end{aligned}$ $\begin{aligned} (2)&&2x +8&=0 \\\\ &&2x &= -8 \\\\ &&x&=-4 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -4 \\\\ \text{greater } x &= -\dfrac{1}{5} \end{aligned}$